Can a displacement texture be unwrapped independent from the image texture?
You need to make two UV maps, use one for displacement and one for the image texture. To do this, go into the mesh properties add hit plus under UV maps:



Now you can edit and update this UV map separatel, be sure to set it for the displace modifier:



Note: when you edit a UV map, you will always be working on the selected one, which is the one highlighted in blue in the UV maps panel. If you need to switch, simply select another one. Also make sure the camera icon is highlighted, as it is by default.